关于弱耦合发展方程组
来源期刊:中南大学学报(自然科学版)1990年第6期
论文作者:杨灵娥
文章页码:658 - 666
关键词:方程组; 弱耦合理论; 非线性; 存在性; 鼓涨
Key words:system of equation; weakly coupling theory; non-linearity; existence; blow up
摘 要:本文我们考虑了一类相当广泛的弱耦合发展方程组的具有齐次Dirichlet边界条件的初边值问题。当方程组是次线性时,利用Galerkin方法我们证明了对任意的初值都存在着整体弱解;当方程组是超线性时,利用凸性理论,我们证明了若初始能量小于零,则局部弱解必在有限时间内爆破。
Abstract: In this peper, we consider the initial boundary value problem with the homogeneous boundarycondition for the generalized systam of weakly coupled evolution equations. If the nonlinearity is sub-linear, by employing Galerkin’s method, it is proved that there exists a global solution for all initial val-ues; if the nonlinearity is superlinear, by using concave arguement, it is proved that if the initial energyis below zero, then the local solutions will blow up in a finite time interval.